Journal
CHAOS SOLITONS & FRACTALS
Volume 140, Issue -, Pages -Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.chaos.2020.110222
Keywords
Fractional nonlinear Schrodinger equation; Levy index; Soliton; Harmonic-oscillator potential
Categories
Funding
- National Natural Science Foundations of China [61675001, 11774068]
- National Theoretical Physics Program [11947103]
- Guangdong Province Nature Foundation of China [2017A030311025]
- Characteristic Innovation Projects of General Colleges and Universities in Guangdong [2019KTSCX083]
- Israel Science Foundation [1286/17]
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We address the existence and stability of localized modes in the framework of the fractional nonlinear Schrodinger equation (FNSE) with the focusing cubic or focusing-defocusing cubic-quintic nonlinearity and a confining harmonic-oscillator (HO) potential. Approximate analytical solutions are obtained in the form of Hermite-Gauss modes. The linear stability analysis and direct simulations reveal that, under the action of the cubic self-focusing, the single-peak ground state and the dipole mode are stabilized by the HO potential at values of the Levy index (the fractionality degree) alpha <= 1, which lead to the critical or supercritical collapse in free space. In addition to that, the inclusion of the quintic self-defocusing provides stabilization of higher-order modes, with the number of local peaks up to seven, at least. (C) 2020 Elsevier Ltd. All rights reserved.
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